Solve each equation for 0 is less than and equal to "x" is less than and equal to 360
3sinx = 2cos^{2}x
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I don't know how to solve this equation...this is what I have, but I don't know if I'm on the right track or not
3sinx = 1 - 2sin^{2}x
3sinx - 1 + 2sin^{2}x = 0
2sin^{2}x + 3sinx - 1 = 0
sinx(3 + 2sinx) = 1
...and if I am, what do I do next now?
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The answers are:
30 and 150 degrees
3sinx = 2cos^2(x)
I believe you've treated this as cos(2x) and expanded it as a double-angle identity. However, you can't do this because the cosine function is being squared. The 2 is not being multiplied by the x.
I'm working on it...
Start by recalling the most important identity. My math teacher calls this "the #1 Identity."
sin^2(x) + cos^2(x) = 1
We want to simplify our trig equation by writing everything in terms of sine. Let's solve the #1 Identity for cos^2(x) because we have that in our trig equation.
cos^2(x) = 1 - sin^2(x)
Plug that into the trig equation, and see what you can get from there. Let me know if you get stuck along the way.
wow I forgot about that identity, thank you!
But, I'm still stuck...
I get
cos^2x + sin^2x = 1
I can't use any compound identities for this...I don't know how to isolate for either cos or sin...
The only identity you need it the #1 Identity.
Plugging in 1 - sin^2(x) for cos^2(x), you should get...
3sinx = 2(1 - sin^2(x))
Use the distributive property, collect everything on the left, and then factor.
The only identity you need is the #1 Identity.
Plugging in 1 - sin^2(x) for cos^2(x), you should get...
3sinx = 2(1 - sin^2(x))
Use the distributive property, collect everything on the left, and then factor.
thanks, I solved it :)
Glad to be of service. :)
Is d answer 90degree
To solve the equation 3sinx = 2cos^2x, you are on the right track with your approach. Let's continue from where you left off:
sinx(3 + 2sinx) = 1
Now, in order to solve for x, we need to find the values of x that satisfy this equation. Let's break it down into two separate cases:
Case 1: sinx = 0
If sinx = 0, then x can be any angle that is a multiple of 180 degrees (or π radians). Since 0 ≤ x ≤ 360, the angle values are 0 and 180 degrees.
Case 2: 3 + 2sinx = 1
Now, let's solve for x in this equation:
2sinx = -2
sinx = -1
To find the angle values for sinx = -1, we can look at the unit circle or trigonometric ratios. The angles where sinx = -1 are 270 and 90 degrees.
So, the solutions for the equation 3sinx = 2cos^2x are x = 0, 180, 270, and 90 degrees.
However, we need to make sure that these solutions satisfy the given condition: 0 ≤ x ≤ 360. Since 270 and 90 degrees fall outside this range, we can eliminate them as valid solutions.
Hence, the final solutions for the equation are x = 0 and 180 degrees.